The properties of ocean waters affect the planning and execution of numerous underwater applications, both military and civilian. One important property is the speed of sound in ocean waters.
The transmission and reception of sound under water is used in many military and civilian applications. Knowledge of the sound speed structure can be of particular importance since it has a direct impact on the way sound energy travels through the ocean. For example, military applications such as underwater sonar and other sensor systems depend on sound energy as the primary method of detecting and locating submarines and mines. Active sonar systems send pulses of sound outward into the water and listen for the returned echo that “bounces” off a target. Passive sonar systems do not actively send out sound signals but instead listen for sound that is transmitted from the target itself, such as the sounds generated by a submarine. In both cases, the structure of the sound speed environment can significantly affect the path and other characteristics of the sound energy, and thus, knowledge of the sound speed structure can be critical to the ability to detect and locate the desired targets. Many civilian industries such as commercial shipping and fishing also utilize sonar in their operations, and thus knowledge of the sound speed structure is equally essential to civilian operations as it is to military ones.
The speed of sound in seawater at any point in the water is dependent on the water's temperature, salinity, and pressure at that point. However, in many parts of the ocean salinity of the water is generally related to its temperature, so that if the temperature of the water and the local temperature-salinity relationship are known, its salinity also can be determined. In addition, sound speed is less sensitive to typical variations in salinity than it is to typical variations in temperature and pressure. For this reason, sound speed in the ocean is often represented as a function of temperature and pressure alone, since salinity can be viewed as being part of the temperature characteristic. As the temperature of the water decreases, so does the speed of sound as it travels through the water. On the other hand, as the water's pressure increases as the depth increases, the speed of sound will increase. However, over typical ranges of upper ocean temperature and pressure variability, the effect of temperature on sound speed is greater than the effect of the pressure.
In addition, there is a depth in the upper ocean, known as the Sonic Layer Depth (SLD), where the sound speed reaches a local maximum. In a simplified representation of the ocean as a warm isothermal surface layer that transitions to a cool deep layer, the SLD is at the base of the isothermal surface layer where sound speed increases due to increasing pressure. In a more complex ocean situation, there may be multiple local maxima and various criteria for identifying a depth as the SLD. Knowing the location of the SLD is important because acoustic energy is refracted away from the SLD, i.e., is refracted upwards above the SLD and refracted downwards below the SLD. Thus, acoustic energy above the SLD tends to stay above that depth, while acoustic energy below tends to stay below. Acoustic energy trapped in a surface duct, i.e., between the surface and the SLD, tends to travel much greater horizontal distances than acoustic energy that spreads into the deep ocean. Consequently, more accurate estimates of the SLD will allow more accurate prediction of ranges of civilian or military acoustic communication and detection.
In addition, the SLD at any point has a corresponding Minimum acoustic Cutoff Frequency (MCF) which affects the behavior of sound between the surface and the SLD. The speed of sound c is related to its frequency f and wavelength λ by the relation f=c/λ. If an SLD exists, then some wavelengths are short enough (frequencies are high enough) to fit in the surface duct above the SLD, while some wavelengths are too long (frequencies too low) to fit in the surface duct. This relationship is generally expressed as an MCF (See, e.g., R. Helber et al., “Evaluating the sonic layer depth relative to the mixed layer depth,” J. Geophys. Res., Vol. 113, C07033, doi:10.1029/2007JC004595, 2008), which depends on the vertical variations of sound speed above the SLD. If the frequency f of a sound is greater than the MCF, its wavelength λ is short enough to fit in the surface acoustic duct between the surface and the SLD. If the frequency of a sound is less than the MCF, then its wavelength will be too long to be trapped, and the sound will penetrate the SLD boundary, where it will attenuate from its source by spherical spreading, with its intensity I decreasing as the inverse square of the distance from the source, i.e.,
      I    =          1              d        2              ,where d is the horizontal distance from the source. On the other hand, if the sound is “trapped” in the acoustic duct between the SLD and the surface (i.e., the frequency f>MCF), it will spread cylindrically, with its intensity decreasing as the simple inverse of the distance, i.e.,
  I  =            1      d        .  Consequently, higher-frequency sound will travel farther horizontally within an acoustic duct than lower-frequency sound, while the lower-frequency sound is free to spread through the vast ocean below the SLD. Since the MCF is dependent on the SLD, having an accurate profile of the location and characteristics of the SLD can be an important factor in knowing and working within the upper ocean's acoustic environment.
Since the SLD is a local sound speed maximum, it may also be the upper bound for an intermediate sound channel or the deep sound channel, sometimes called the Sound Fixing and Ranging (SOFAR) channel. These subsurface channels trap acoustic energy based on downward refraction above and upward refraction below. There is a minimum frequency that can be trapped in the subsurface sound channel, and while this minimum frequency depends on the thickness of and sound speed structure in the subsurface channel, the formulation differs from the surface duct that has reflection from the ocean surface. Identification of intermediate or deep sound channels is important because acoustic energy trapped in the channels travels much greater horizontal distances than acoustic energy at frequencies too low to be trapped.
The SLD defines the base and many other characteristics of the surface acoustic duct, and may also define the location of the upper boundary of the possible intermediate or deep sound channels. Knowing the location and properties of an acoustic duct can influence many decisions relating to underwater operations, and particularly can influence decisions regarding the placement of objects underwater.
For example, this knowledge can be an important aspect determining the placement of underwater acoustic sensors. Sensors will best detect sound emanating from their targets if they are placed on the same side of the SLD boundary (i.e., temperature interface) as the target. On the other hand, if the goal of object placement is to “hide”the object, such as may be the case with determining the travel path of a submarine, the object is best placed on the opposite side of the SLD boundary, since the SLD boundary can act to insulate the sound from detection, for example, from surface-based sensors. Conversely, knowing the SLD at any particular point in the ocean, and thus the MCF at that point, can permit operators to “tune” their equipment to the appropriate frequency to enable detection or hiding of an object, as the case may be. Acoustic communication is affected in the same manner as acoustic detection. Thus, for all of these reasons, it is highly desirable to obtain accurate information regarding the SLD and the vertical and horizontal structure of sound speed in the water.
Another important characteristic of the ocean is its Mixed Layer Depth (MLD). The MLD is the thickness of the water's surface layer that has a nearly constant temperature, salinity, and density due to turbulent mixing at the top of the layer and shear at the bottom. Information regarding the MLD can be obtained by direct sensing, for example, as measured by Conductivity-Temperature-Depth (CTD) recorders on a variety of platforms throughout the global ocean. Information regarding the MLD can also be estimated by use of ocean models such as the LDNK06 or KRH00 ocean models, which can estimate the MLD based on measured readings of temperature, salinity, or both. See, e.g., R. Helber et al., “Evaluating the sonic layer depth relative to the mixed layer depth,” J. Geophys. Res., Vol. 113, C07033, doi: 10.1029/2007JC004595, 2008.
Other ocean models also are used to provide estimates of ocean properties when accurate real-time data are available. The modular ocean data assimilation system (MODAS) has been developed to meet the U.S. Navy's need for rapid estimates of present and near-term ocean conditions, particularly in situations where little or no in situ data are not available. MODAS comprises a collection of programs and utilities for combining remotely sensed data and in situ measurements to create a synthetic profile of ocean conditions such as temperature and salinity and of derived aspects such as density, sound speed, and mixed layer depth. D.N. Fox et al., 2002, “The Modular Ocean Data Assimilation System,”Oceanography, Vol. 15, pp. 22-28; D.N. Fox et al., 2002, “The Modular Ocean Data Assimilation System (MODAS),” J. Atm and Oceanic Tech., Vol. 19, pp. 240-252.
MODAS synthetic profiles are produced based on climatological average temperature, climatological relationships between temperature and salinity, real-time estimates of sea surface temperature (SST), real-time estimates of sea-surface height (SSH), and climatological regression coefficients used in a polynomial that expresses a temperature difference at a series of depths as a function of SSH and SST. The mean temperature profile and regression coefficients are defined at up to 36 standard depths at each point in a variable horizontal grid from one to ⅛ degree spacing in latitude and longitude. The coefficients are defined using a regression model to minimize the expected squared errors of temperature. The regression coefficients, climatological averages and coefficients to predict salinity from temperature are defined every-other month based on minimizing the expected squared errors using the synthetics to model millions of historical observations.
Ocean modeling systems such as MODAS can also be used to estimate the SLD of an area of interest using synthetic profiles of the ocean's temperature and salinity for that area. However, modeled estimates of the SLD based on such synthetic profiles lead to a shallow bias in the estimates of the sonic layer depth and a corresponding high bias in estimates of the minimum cutoff frequency of acoustic signals propagated in the surface acoustic duct.